(26steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc

At: finite-partition 2 1 2

1. n:
2. 0 < n
3. k:
4. c: nk
5. p: k( List)
6. sum(||p(j)|| | j < k) = n-1
7. j:k, x,y:||p(j)||. x < y (p(j))[x] > (p(j))[y]
8. j:k, x:||p(j)||. (p(j))[x] < n-1 & c((p(j))[x]) = j
sum(if c(n-1)=j ||[(n-1) / (p(j))]|| else ||p(j)|| fi | j < k) = n

By:
Reduce 0
THEN
RWO Thm* k:, f,g:(k), p:(k). sum(if p(i) f(i)+g(i) else f(i) fi | i < k) = sum(f(i) | i < k)+sum(if p(i) g(i) else 0 fi | i < k) 0
THEN
HypSubst' -3 0


Generated subgoal:

1 n-1+sum(if c(n-1)=j 1 else 0 fi | j < k) = n5 steps

About:
listconsboolifthenelseintnatural_number
addsubtractless_thanapplyfunctionequalimpliesall

(26steps total) PrintForm Definitions Lemmas graph 1 2 Sections Graphs Doc